n and p are the densities of the electrons in the conduction band and holes in the valence band, respectively, and μ e and μ p are the electron and hole mobilities, respectively.
Figure 1.8 shows the band structure of intrinsic, p‐type, and n‐type semiconductors. For example, when Si is doped with a pentavalent element like P or As, electrons are generated in the conduction band. It thus becomes an n‐type extrinsic semiconductor. Instead, when the doping element is a trivalent element like B, Al, or Ga, holes are generated in the valence band. The semiconductor becomes a p‐type extrinsic semiconductor. Although doping can increase the charge carrier density, it also shifts the Fermi level. The n‐type doping shifts the Fermi level upward to the conduction band, while p‐doping shifts the Fermi level downward to the valence band. Because the Seebeck coefficient of a lightly doped semiconductor is related to the energy difference between the bottom of the conduction band and the Fermi level for a n‐type semiconductor and between the top of the valence band and the Fermi level for a p‐type semiconductor. Therefore, increasing the doping level can increase the electrical conductivity but lower the Seebeck coefficient.
Figure 1.8 Band structures of (a) intrinsic, (b) n‐type, and (c) p‐type semiconductors.
The conductivity of intrinsically conducting polymers can be dramatically increased by doping as well. But the nature of the doping for conducting polymers is fundamentally different from that of inorganic semiconductors. The doping of the former involves the oxidation or reduction of the conjugated backbone, while that of the latter arises from the ionization of the doping elements. Doping does not produce any new band in inorganic semiconductors. But new energy levels or bands are generated in conducting polymers after doping because the charge carriers including electrons and holes in doped inorganic semiconductors can be considered as free electrons while the charge carriers of conducting polymers strongly couple with the lattice vibration.
Because of the strong coupling between the electrons and lattice vibration, the charge carriers in conducting polymers are related to their symmetry. The charge carriers in doped polyacetylene are solitons because of its high symmetry in the chemical structure. A soliton has a positive charge when it is oxidative doping of polyacetylene, and the charge is negative when it is reductive doping (Figure 1.9). The solitons are delocalized along the conjugated polymer backbone. As shown in Figure 1.10, there is a discrete soliton level between the conduction band and valence band at low doping level. There is no electron on the soliton level if oxidative doping occurs for polyacetylene, and there are two electrons on the soliton level when it is reductive doping. When the doping degree is high enough, the solitions couple with each other and the soliton level becomes a continuous soliton band.
The symmetry of the chemical structure of other conducting polymers such as polypyrrole (PPy), polythiophene (PTh), and polyaniline (PANi) is lower than that of polyacetylene. Their charge carriers are polarons at low doping degree. As shown in Figure 1.11, there is a positive charge and an electron for a polaron. Because a polaron mainly involves two atoms, there are two polaron levels between the conduction band and valence band (Figure 1.12). The electron is on the lower polaron level. At the medium doping degree, the polarons can interact with each other, and two polarons become a bipolaron. A bipolaron has two positive charges and no electron. At high doping degree, the bipolarons couple each other, and the two bipolaron levels turn to two continuous bipolaron bands.
Figure 1.9 Polyacetylene (PA) with (a) a positive soliton and (b) a negative soliton.
Figure 1.10 Structures of polyactylene in (a) neutral state, (b) low doping degree and, (c) high doping degree.
Figure 1.11 Polythiophene with (a) a polaron and (b) a bipolaron.
Figure 1.12 Band structures of conducting polymers with less symmetry in (a) neutral state, (b) low doping degree, (c) medium doping degree, and (d) high doping degree. There is one electron on the lower polaron level in (b), while no electron on the bipolaron levels and bipolaron bands in (c) and (d).
1.1.5.2 Charge Carrier Mobility
The conduction electrons in metals are the valence electrons of metal atoms. The conduction electrons can be scattered by the lattice consisted of metal cations, and the lattice scattering lowers the electron mobility. Because of the much higher ion concentration in metals than in inorganic semiconductors, metals usually have a much lower charge carrier mobility than inorganic semiconductors. The charge carrier mobility of inorganic semiconductors is mainly affected by impurities, defects, and lattice vibration. A doping atom can be considered as an impurity, and it forms a scattering center for the charge carriers. As a result, doping lowers the charge carrier mobility. Therefore, the charge carrier mobility of inorganic semiconductor and conducting polymers usually decreases with the increasing doping level.
Different from metals and inorganic semiconductor that can be prefect crystals, a conducting polymer cannot have 100% crystallinity. There are both amorphous and crystalline domains in conducting polymers (Figure 1.13). The amorphous domain has a conductivity much lower than that of the crystalline domain. The charge transports include intrachain, interchain, and inter‐domain processes. The interchain charge transport is usually the dominant process. Thus, the charge carrier mobility of conducting polymers strongly depends on the crystallinity. High crystallinity can facilitate the interchain charge transport, and thus give rise to high charge carrier mobility. A conducting polymer with the same chemical composition can have conductivities spanning several orders by magnitude.
Figure 1.13 (a) Intrachain, (b) interchain, and (c) inter‐domain charge transports in conducting polymers.
The